scholarly journals Shear-free boundary in Stokes flow

1996 ◽  
Vol 19 (1) ◽  
pp. 145-150 ◽  
Author(s):  
D. Palaniappan ◽  
S. D. Nigam ◽  
T. Amaranath
Keyword(s):  
Free Boundary ◽  
Stokes Flow ◽  
Axially Symmetric ◽  
Symmetric Flow ◽  
Stream Surface ◽  
Flow Past ◽  
Flow Past A Sphere

A theorem of Harper for axially symmetric flow past a sphere which is a stream surface, and is also shear-free, is extended to flow past a doubly-body𝔅consisting of two unequal, orthogonally intersecting spheres. Several illustrative examples are given. An analogue of Faxen's law for a double-body is observed.

Slow viscous flow past a rotating sphere

1971 ◽  
Vol 69 (2) ◽  
pp. 333-336 ◽  
Author(s):  
K. B. Ranger
Keyword(s):  
Stokes Flow ◽  
Rotating Fluid ◽  
Axially Symmetric ◽  
Asymmetric Flow ◽  
Symmetric Flow ◽  
Reversed Flow ◽  
Linear Superposition ◽  
Rotating Sphere ◽  
Flow Past ◽  
Uniform Stream

Keller and Rubinow(l) have considered the force on a spinning sphere which is moving through an incompressible viscous fluid by employing the method of matched asymptotic expansions to describe the asymmetric flow. Childress(2) has investigated the motion of a sphere moving through a rotating fluid and calculated a correction to the drag coefficient. Brenner(3) has also obtained some general results for the drag and couple on an obstacle which is moving through the fluid. The present paper is concerned with a similar problem, namely the axially symmetric flow past a rotating sphere due to a uniform stream of infinity. It is shown that leading terms for the flow consist of a linear superposition of a primary Stokes flow past a non-rotating sphere together with an antisymmetric secondary flow in the azimuthal plane induced by the spinning sphere. For a3n2 > 6Uv, where n is the angular velocity of the sphere, U the speed of the uniform stream, and a the radius of the sphere, there is in the azimuthal plane a region of reversed flow attached to the rear portion of the sphere. The structure of the vortex is described and is shown to be confined to the rear portion of the sphere. A similar phenomenon occurs for a sphere rotating about an axis oblique to the direction of the uniform stream but the analysis will be given in a separate paper.

Axisymmetric Stokes flow past a spherical cap

1976 ◽  
Vol 75 (2) ◽  
pp. 273-286 ◽  
Author(s):  
J. M. Dorrepaal ◽  
M. E. O'neill ◽  
K. B. Ranger
Keyword(s):  
Vortex Ring ◽  
Stokes Flow ◽  
Concave Surface ◽  
Local Velocity ◽  
Oncoming Flow ◽  
Spherical Cap ◽  
Stream Surface ◽  
Flow Past ◽  
Mainstream Flow

The axisymmetric streaming Stokes flow past a body which contains a surface concave to the fluid is considered for the simplest geometry, namely, a spherical cap. It is found that a vortex ring is attached to the concave surface of the cap regardless of whether the oncoming flow is positive or negative. A stream surface ψ = 0 divides the vortex from the mainstream flow, and a detailed description of the flow is given for the hemispherical cup. The local velocity and stress in the vicinity of the rim are expressed in terms of local co-ordinates.

Axially symmetric flow with free boundary

1995 ◽  
Vol 47 (4) ◽  
pp. 555-566 ◽  
Author(s):  
A. S. Minenko
Keyword(s):  
Free Boundary ◽  
Axially Symmetric ◽  
Symmetric Flow

scholarly journals Analytical solutions of compacting flow past a sphere

2014 ◽  
Vol 746 ◽  
pp. 466-497 ◽  
Author(s):  
John F. Rudge
Keyword(s):  
Analytical Solutions ◽  
Stokes Flow ◽  
Solid Matrix ◽  
Rigid Sphere ◽  
Deformable Solid ◽  
Two Phase ◽  
Low Viscosity ◽  
Flow Past ◽  
Phase Medium ◽  
Flow Past A Sphere

AbstractA series of analytical solutions are presented for viscous compacting flow past a rigid impermeable sphere. The sphere is surrounded by a two-phase medium consisting of a viscously deformable solid matrix skeleton through which a low-viscosity liquid melt can percolate. The flow of the two-phase medium is described by McKenzie’s compaction equations, which combine Darcy flow of the liquid melt with Stokes flow of the solid matrix. The analytical solutions are found using an extension of the Papkovich–Neuber technique for Stokes flow. Solutions are presented for the three components of linear flow past a sphere: translation, rotation and straining flow. Faxén laws for the force, torque and stresslet on a rigid sphere in an arbitrary compacting flow are derived. The analytical solutions provide instantaneous solutions to the compaction equations in a uniform medium, but can also be used to numerically calculate an approximate evolution of the porosity over time whilst the porosity variations remain small. These solutions will be useful for interpreting the results of deformation experiments on partially molten rocks.

Stokes flow past a sphere coated with a thin fluid film

1981 ◽  
Vol 110 ◽  
pp. 217-238 ◽  
Author(s):  
Robert Edward Johnson
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Stokes Flow ◽  
Fluid Layer ◽  
Fluid Film ◽  
Fluid Viscosity ◽  
Flow Past ◽  
Surface Tension Forces ◽  
Force Equilibrium ◽  
Flow Past A Sphere

The present study examines the steady, axisymmetric Stokes flow past a sphere coated with a thin, immiscible fluid layer. Inertial effects are neglected for both the outer fluid and the fluid film, and surface tension forces are assumed large compared with the viscous forces which deform the fluid film. Furthermore, the present analysis assumes that the mechanism driving the fluid circulation within the film is not too large. From force equilibrium on the film we find that a steady fluid film can only partially cover the sphere, i.e. the film must be held to the sphere by surface tension forces at the contact line. The extent of the sphere covered by the film is specified, in terms of the solid–fluid contact angle, by the condition of global force equilibrium on the fluid film.Using a perturbation scheme based on the thinness of the fluid layer the solution to the flow field is obtained analytically, except for the fluid-film profile (i.e. the fluid–fluid interface) which requires numerical calculations. One of the principal results is an expression for the drag force on the fluid-coated particle. In particular, we find that the drag on a sphere is reduced by the presence of a fluid coating when the ratio of the film fluid viscosity to the surrounding fluid viscosity is less than ¼. Detailed numerical computations are conducted for a few typical cases. The calculations show that a film of prescribed areal extent, i.e. specified contact angle, is only possible when the magnitude of the driving force on the film is below some maximum value. A simple experiment was also performed, and photographs, which qualitatively illustrate the fundamental fluid-film configurations predicted by the theory, are presented.

Stability of the O(2)‐symmetric flow past a sphere in a pipe

1994 ◽  
Vol 6 (12) ◽  
pp. 3884-3892 ◽  
Author(s):  
S. J. Tavener
Keyword(s):  
Symmetric Flow ◽  
Flow Past ◽  
Flow Past A Sphere

Stokes flow past a sphere with mixed slip-stick boundary conditions

1993 ◽  
Vol 11 (5) ◽  
pp. 229-234 ◽  
Author(s):  
B S Padmavathi ◽  
T Amaranath ◽  
S D Nigam
Keyword(s):  
Boundary Conditions ◽  
Stokes Flow ◽  
Flow Past ◽  
Flow Past A Sphere

Higher-Order Compact Scheme for the Incompressible Navier-Stokes Equations in Spherical Geometry

2012 ◽  
Vol 11 (1) ◽  
pp. 99-113 ◽  
Author(s):  
T. V. S. Sekhar ◽  
B. Hema Sundar Raju ◽  
Y. V. S. S. Sanyasiraju
Keyword(s):  
Stokes Equations ◽  
Higher Order ◽  
Compact Scheme ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Uniform Grid ◽  
Axially Symmetric ◽  
Flow Past ◽  
Correction Technique ◽  
Flow Past A Sphere

AbstractA higher-order compact scheme on the nine point 2-D stencil is developed for the steady stream-function vorticity form of the incompressible Navier-Stokes (N-S) equations in spherical polar coordinates, which was used earlier only for the cartesian and cylindrical geometries. The steady, incompressible, viscous and axially symmetric flow past a sphere is used as a model problem. The non-linearity in the N-S equations is handled in a comprehensive manner avoiding complications in calculations. The scheme is combined with the multigrid method to enhance the convergence rate. The solutions are obtained over a non-uniform grid generated using the transformation r=e? while maintaining a uniform grid in the computational plane. The superiority of the higher order compact scheme is clearly illustrated in comparison with upwind scheme and defect correction technique at high Reynolds numbers by taking a large domain. This is a pioneering effort, because for the first time, the fourth order accurate solutions for the problem of viscous flow past a sphere are presented here. The drag coefficient and surface pressures are calculated and compared with available experimental and theoretical results. It is observed that these values simulated over coarser grids using the present scheme are more accurate when compared to other conventional schemes. It has also been observed that the flow separation initially occurred at Re = 21.

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